Exploratory Subgroup Analyses in Clinical Research by Rosenkranz Gerd;

Author:Rosenkranz, Gerd; [Rosenkranz, Gerd]
Language: eng
Format: epub
Publisher: John Wiley & Sons, Incorporated
Published: 2020-01-08T16:00:00+00:00

one obtains with

and

Equations (4.4) and (4.5) of the previous chapter can now be easily obtained:

In the remaining part of this and in the next section we will derive results for EB estimates from Theorem 5.1 above.

Corollary 5.1

Under the conditions of Theorem 5.1 it follows:

is non‐decreasing in .

if the marginal distribution 5.1 is log concave.

Proof

The first assertion follows from 5.2, 5.3 and

the second is immediate from 5.3.

It was shown above that is log concave for the model with a normal prior. However this condition is not generally fulfilled for general priors like the mixture priors considered in the next section. This implies that the uniform variance reduction does not hold in general as will become obvious as a consequence of Corollary 5.2 and from the analysis of a dataset in Section 5.4.3.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.